Helical trilayer graphene: a moir\'e platform for strongly-interacting topological bands

Quantum geometry of electronic wavefunctions results in fascinating topological phenomena. A prominent example is the intrinsic anomalous Hall effect (AHE) in which a Hall voltage arises in the absence of an applied magnetic field. The AHE requires a coexistence of Berry curvature and spontaneous time-reversal symmetry breaking. These conditions can be realized in two-dimensional moir\'e systems with broken $xy$-inversion symmetry ($C_{2z}$) that host flat electronic bands. Here, we explore helical trilayer graphene (HTG), three graphene layers twisted sequentially by the same angle forming two misoriented moir\'e patterns. Although HTG is globally $C_{2z}$-symmetric, surprisingly we observe clear signatures of topological bands. At a magic angle $\theta_\mathrm{m}\approx 1.8^\circ$, we uncover a robust phase diagram of correlated and magnetic states using magnetotransport measurements. Lattice relaxation leads to large periodic domains in which $C_{2z}$ is broken on the moir\'e scale. Each domain harbors flat topological bands with valley-contrasting Chern numbers $\pm(1,-2)$. We find correlated states at integer electron fillings per moir\'e unit cell $\nu=1,2,3$ and fractional fillings $2/3,7/2$ with the AHE arising at $\nu=1,3$ and $2/3,7/2$. At $\nu=1$, a time-reversal symmetric phase appears beyond a critical electric displacement field, indicating a topological phase transition. Finally, hysteresis upon sweeping $\nu$ points to first-order phase transitions across a spatial mosaic of Chern domains separated by a network of topological gapless edge states. We establish HTG as an important platform that realizes ideal conditions for exploring strongly interacting topological phases and, due to its emergent moir\'e-scale symmetries, demonstrates a novel way to engineer topology.